论文简报
cs.LG 2605.26808v1 值得读

Innovation: An Almost Characterization of Hallucination

Nishant P. Das, Piyush Srivastava

发布日期：2026-05-26 10:24 相关性：0.7000 价值：0.7600 分类：cs.LG cs.AI cs.IT
arXiv 摘要 PDF 原文 网页正文

摘要

Hallucination is a central limitation of large language models (LLMs), and substantial effort has been devoted to understanding and mitigating it. Towards this, Kalai and Vempala (STOC 2024) introduced a probabilistic framework formalizing calibration and hallucination, and showed that, with high probability, calibrated LLMs hallucinate roughly at the rate of the "missing mass", a measure of how incomplete the training data is relative to its source. This raises two fundamental questions: (i) what property of a calibrated LLM makes hallucinations unavoidable? and (ii) can hallucinations be avoided by giving up calibration? We answer these questions by introducing a simpler property we call innovation that measures the tendency of a model to produce outputs outside the training data. We show that innovation is implied by the condition for hallucination identified by Kalai and Vempala, and, further, that it is an almost characterization of hallucination: hallucination implies innovation, and conversely, innovation implies hallucination with high probability. We also provide lower bounds on the hallucination rate based on the "innovation rate", and by relating innovation rate back to missing mass, we obtain new hallucination rate lower bounds based on missing mass that extend the results of Kalai and Vempala.

相关性判断

medium
相关方向
statistical_learning information_theory_adjacent probability
判断依据

The paper is mainly about LLM hallucination, but it explicitly falls under cs.IT and uses probabilistic quantities like missing mass, calibration, and lower bounds that are adjacent to information-theoretic/statistical analysis, so it is worth later review.

价值判断

Clear theoretical contribution: introduces innovation as an almost characterization of hallucination within the Kalai-Vempala probabilistic framework. Strong structure evidence with precise assumptions, main claims, and technical tools including lower bounds, calibration/coarsening, missing-mass translation, and high-probability arguments. Relevant to cs.IT-adjacent statistical learning and probability, though the primary category and motivation are LLM hallucination rather than core information theory.

核心问题与主要方法

核心问题

Characterize when hallucination is unavoidable for LLMs and derive rate lower bounds

场景：Kalai-Vempala probabilistic framework for unprompted LLM generation over a finite statement space with a corpus sampled from a latent document distribution

主要方法

Defines innovation as g(U) > 0, where U is the complement of the observed training support, separating extrapolation beyond the corpus from calibration. Uses K-sparsity and Regular Facts to bound the posterior probability that any chosen unseen statement is factual by roughly K/|U|, so unseen model mass is likely hallucination mass. Shows calibration plus positive missing mass forces positive probability on an unseen factual statement through partition coarsening, hence implies innovation. Derives hallucination-rate lower bounds from innovation rate using a Markov-style expectation argument and a high-confidence case analysis based on the maximum probability assigned to any unseen statement. Relates innovation rate to missing mass through total variation distance between the model distribution and a coarsened document distribution, yielding missing-mass lower bounds under weaker assumptions than some prior bounds.

关键贡献与后续阅读

关键贡献

Introduces innovation rate as a simpler model-and-corpus statistic that nearly characterizes hallucination existence in the Kalai-Vempala framework. Strictly generalizes the existence-level calibration-implies-hallucination route by showing calibration with any positive missing mass implies innovation, then innovation implies hallucination with high probability. Provides lower bounds on hallucination rate directly in terms of innovation rate, including bounds that avoid the corpus-size dependence present in baseline Kalai-Vempala bounds under only K-sparsity and Regular Facts. Connects innovation-rate bounds back to missing mass via coarsening and total variation, producing new missing-mass hallucination lower bounds that remain nonvacuous in regimes where prior bounds may collapse. Adds exploratory evidence that innovation and hallucination rates align in controlled n-gram settings, supporting but not proving robustness beyond the formal assumptions.

研究启发

What are the exact constants and probability levels in Theorems 3.3, 4.1, and 4.2 after parsing the rendered formulas from the PDF/source? How sensitive are the results to violations of Regular Facts in realistic semantic or prompted settings? Can the semantic innovation estimator proposed with sentence embeddings be related to any formal relaxed version of the finite-support theory? Do the missing-mass translation bounds remain quantitatively useful when K is large relative to realistic statement spaces?

限制与不确定性

Model is abstract and depends on finite statement-space, K-sparsity, Regular Facts, and i.i.d. corpus assumptions. Empirical evidence appears toy n-gram based, not a direct validation on modern LLM behavior. Value for an information theory workflow is medium rather than urgent because the main framing is LLM reliability.

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